1. Field of the Invention
The present invention generally relates to a deflection mirror adopting a micro-machining technology, and an optical writing apparatus and an image formation apparatus therewith. The present invention especially relates to a deflection mirror wherein a mirror substrate supported by beams is driven by electrostatic force, and the mirror substrate vibrates with the beam being at the center; and an optical writing apparatus and an image formation apparatus therewith.
2. Description of the Related Art
According to a deflection mirror indicated by Non-Patent Reference 1, a mirror substrate is supported by two beams that are on the same straight line, and is reciprocated (vibrates) with the two beams serving as the axle of torsional rotation by electrostatic attraction between an electrode and the mirror substrate, the electrode facing the mirror substrate. This deflection mirror manufactured by the micro machining technology has features such as it is easy to miniaturize, its manufacturing cost is low, and the structure is simple as compared with optical scanners structured by a polygon mirror that is rotated by a motor, because the deflection mirror can be packaged as a semiconductor device. Further, a polygon mirror has a problem of precision between mirror faces. This problem is not a concern in the case of a deflection mirror. Furthermore, the deflection mirror is capable of high-speed scanning by reciprocation.
Other deflection mirrors that are driven by electrostatic force have been known as follows: a deflection mirror wherein a beam is shaped like a character “S”, and rigidity is lowered such that a great deflection angle is obtained by small driving force (Patent Reference 1); a deflection mirror wherein the thickness of a beam is made smaller than the thickness of a mirror substrate and a frame substrate (Patent Reference 2); a deflection mirror wherein a driver electrode is arranged in a position that does not overlap with the vibrating direction of a mirror unit (Patent Reference 3 and Non-Patent Reference 2); and a deflection mirror wherein a driving electrode is arranged with an inclination from the central position of vibration of the mirror, lowering a driving voltage without changing the deflection angle of the mirror (Non-Patent Reference 3).
While the deflection mirrors described above use electrostatic attraction, other deflection mirrors that use electromagnetic force and a piezoelectric device as driving means are also devised.
Generally, these deflection mirrors that include a mirror substrate and a torsional (twisting) beam are driven so that a great deflection angle may be acquired with low energy, and the mirror substrate may be vibrated by a resonance frequency of the structure determined by material, form, and size of the mirror substrate and the torsional (twisting) beam.
[Patent Reference 1] Patent JP 2924200
[Patent Reference 2] JPA, 7-92409
[Patent Reference 3] Patent JP 3011144
[Non-Patent Reference 1] K. E. Petersen, “Silicon Torsional Scanning Mirror”, IBM Journal of Research and Development 24, 1980, pp. 631–637
[Non-Patent Reference 2] Harald Schenk, “An Electrostatically Excited 2D-Micro-Scanning-Mirror with an In-Plane configuration of the Driving Electrodes”, The 13th Annual International Workshop on MEMS 2000, (2000), pp. 473–478
[Non-Patent Reference 3] Henri CAMON, et al. “Fabrication, Simulation and Experiment of a Rotating Electrostatic Silicon Mirror with Large Angular Deflection”, The 13th Annual International Workshop on MEMS 2000, (2000), pp. 645–650
In the case of a deflection mirror wherein a fixed driving electrode is arranged to counter a free side (a side that is not supported by the beam) of the mirror substrate, an area of the driving electrode can be made great by forming the free side (acting as a movable electrode) of the mirror substrate and the fixed driving electrode in the shape of comb-teeth such that they gear through (mesh without contacting) at a minute gap. The inventor hereto has filed Patent applications of deflection mirrors using the comb-teeth shaped electrode, e.g., JPA 2003-143326. Therein, the comb-teeth shaped fixed electrode is divided into two stages, namely an upper stage and a lower stage. In this manner, a stable and great deflection angle of the reciprocal vibration is obtained even if the vibration becomes out of the resonance point of the mirror substrate.
Here, a deflection angle θ of the mirror substrate is expressed by the following formulaθ=fK(ω, δ)/I, where
f represents electrostatic force between the free side (movable electrode) of the mirror substrate and the fixed electrode,
ω represents an angular velocity
δ represents viscosity resistance of the vibration space of the mirror substrate, and
I represents moment of inertia of the mirror substrate.
Accordingly, if the electrostatic force is increased, the angle θ increases.
Further, the following formula gives the electrostatic force f,f=½[εo(V/d)^2S], where
d represents a gap length between electrodes,
V represents a voltage between the electrodes,
εo represents the dielectric constant of vacuum, and
S represents the area of the electrode.
The formula shows that the greater the electrode area, and the smaller the gap between electrodes, the greater the electrostatic force is.
Now, the mirror substrate is subject to deformation when vibrating by the moment of inertia. The deformation of the mirror substrate has direct influence on the quality of an optical beam reflected by the mirror substrate. It is required that the deformation of the mirror substrate be suppressed as much as possible, especially where the deflection mirror is used by a writing optical system, such as a laser beam printer that requires highly precise diameter and intensity distributions of the beam. For this purpose, it is effective to increase the thickness of the mirror substrate and to raise rigidity. However, this increases the mass, so that the moment of inertia of the mirror substrate increases, requiring higher driving electrostatic force, i.e., requiring a higher driving voltage.